Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#89683 | C2 | semidirect |
| 2. #11739227 | C2 | semidirect |
| 3. D7×#493 | C2 | semidirect |
| 4. C7×#2246 | C2 | semidirect |
| 5. #11729220 | C2 | semidirect |
| 6. #11729045 | C2 | semidirect |
| 7. #11729044 | C2 | semidirect |
| 8. #11726815 | C2 | semidirect |
| 9. C4×#6372 | C2 | semidirect |
| 16. C2×C7×D16 | C22 | semidirect |
| 18. C7×#493 | C22 | semidirect |
| 20. #89927 | C22 | semidirect |
| 23. C2×#6401 | C22 | semidirect |
| 24. C2×#6400 | C22 | semidirect |
| 28. C2×#6374 | C22 | semidirect |
| 30. #89471 | C22 | semidirect |
| 33. C4×C7×C16 | C22 | semidirect |
| 34. #89297 | C22 | semidirect |
| 35. C4×C7⋊C16 | C22 | semidirect |
| 78. #6372 | D4 | semidirect |
| 86. #2246 | D7 | semidirect |
| 130. C7×C16 | C2×D4 | semidirect |
| 131. C7⋊C16 | C2×D4 | semidirect |
| 142. C2×D16 | C2×D7 | semidirect |
| 152. #493 | C2×D7 | semidirect |
| 157. C4×C16 | C2×D7 | semidirect |
| 243. C4×C7 | #509 | semidirect |
| 292. C16 | D4×D7 | semidirect |
| 332. C7 | #33717 | semidirect |
| 346. C4 | #89683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89683 | 2 |
| #11739227 | 2 |
| D7×#493 | 2 |
| C7×#2246 | 2 |
| #11729220 | 2 |
| #11729045 | 2 |
| #11729044 | 2 |
| #11726815 | 2 |
| C4×#6372 | 2 |
| #33717 | 7 |